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Fundamental researches
UDC: 616.12-008:004.891.3 DOI: 10.26565/2313-6693-2022-45-01
ENTROPY OF FREQUENCY DOMAIN OF HEART RATE
VARIABILITY
Martynenko O.A B C,D E F, Raimondi G.A E F, Barsi L.E F, MaliarovaL.E F
A - research concept and design; B - collection and/or assembly of data; C - data analysis and
interpretation; D - writing the article; E - critical revision of the article; F - final approval of the article
Introduction. The heart rate variability (HRV) is based on measuring (time) intervals between R-peaks (of RR-intervals) of an electrocardiogram (ECG) and plotting a rhythmogram on their basis with its subsequent analysis by various mathematical methods which are classified as Time-Domain (TD), Frequency-Domain (FD) and Nonlinear [1, 2]. There are a number of popular Nonlinear methods used in HRV analysis, such as entropy-based measures that mostly applied for TD. Spectral Entropy (SE) is using for Frequency-Domain: it is defined to be the Shannon entropy of the power spectral density (PSD) of the data. An important characteristic of Frequency-Domain studies is sympatho-vagal balance, which has been overlooked by entropy-based analysis. This is due to the fact that good entropy analysis restricted the number of existing HRV data, which is shrinking in FD and also in total spectrum parts.
Aim of the research. The goal of this paper is to provide a reliable formula for calculating entropy accurately for Frequency-domain of standard 5-min. HRV records and to show the advantages of such approach for analyzing of sympatho-vagal balance for healthy subjects (NSR), Congestive Heart Failure (CHF) and Atrial Fibrillation (AF) patients.
Materials and Methods. We used MIT-BIH long-term HRV records for Normal Sinus Rhythm (NSR), Congestive Heart Failure (CHF) and Atrial Fibrillation (AF).
The generalized form of the Robust Entropy Estimator (EnRE) for Frequency-domain of standard 5-min. HRV records was proposed and the key EnRE futures was shown.
The difference between means of the two independent selections (NSR and CHF, before and after AF) has been determined by a t-test for independent samples; discriminant analysis and statistical calculations have been done by using the statistical package IBM SPSS 27.
The results of the study. We calculate entropy for all valuable for HRV spectral interval, namely 00.4 Hz and to compare with existing results for Spectral Entropy: qualitatively we receive the same distribution number as [14] and significant difference (p < 0.001) between entropy averages for NSR and CHF or AF patients.
We define low-frequencies (LF) power spectrum components in the range of 0.04-0.15 Hz and high-frequencies (HF) power spectrum components in the range of 0.15-0.4 Hz [1]. The sympatho-vagal balance is a simple ratio LF/HF [1]. Then, we define an entropy eLF of the LF power spectrum components, an entropy eHF of the HF power spectrum components and entropy based sympatho-vagal balance as a ratio eLF/eHF.
The difference between NSR and CHF groups are significant in both cases LF/HF and eLF/eHF with p < 0.001, but in case of eLF/eHF the results are quite better (t = -4.8, compared to LF/HF where t = -4.4). The discriminant analysis shows total classification accuracy for eLF/eHF in 79.3 % (x2 = 19.4, p < 0.001) and for LF/HF in 72.4 % (x2 = 16.6, p < 0.001).
We applied entropy-based Frequencies-domain analyzing for AF patients and showed that ratio eLF/eHF is significantly higher during AF than before AF (p < 0.001). This is opposite to ordinary LF/HF where difference is insignificant due to high variation of this ratio.
Conclusion. Proposed in the article is generalized form for Robust Entropy Estimator EnRE for Frequencies-domain, which allows, for time series of a limited length (standard 5-min. records), to find entropy value of HRV power spectrum (total spectrum, low- and high- frequencies bands).
Using the proposed EnRE for MIT-BIH database of HRV records, we show for standard 5 min. HRV records the usage of EnRE of HRV power spectrum and entropy-based sympatho-vagal balance of Normal Sinus Rhythm (NSR) and Congestive Heart Failure (CHF) cases. It is demonstrated, that, entropy-based Frequencies-domain analyzing is applicable for case of Atrial Fibrillation (AF) even during AF episodes. We showed the significant difference (p < 0.001) before and during AF for entropy of total spectrum, as well as for sympatho-vagal balance in form of eLF/eHF.
KEY WORDS: hearth rate variability, entropy, frequency-domain, congestive heart failure, atrial fibrillation
© Martynenko O., Raimondi G., Barsi L., Maliarova L., 2022
INFORMATION ABOUT AUTHORS
Martynenko Oleksandr Vitalyevich, D.Sc., Ph.D., Full Professor, Department of Hygiene and Social Medicine, School of Medicine, V. N. Karazin Kharkiv National University, 6, Svobody sq., Kharkiv, Ukraine, 61022. e-mail: Alexander.v.martynenko@karazin.ua, ORCID ID: https://orcid.org/0000-0002-0609-2220.
Gianfranco Raimondi, MD, PhD, Prof., Sapienza University of Rome (Italy), 5, Piazzale Aldo Moro, Rome, Italy,
00185; e-mail: gianfrancoraimondi@uniroma1.it
Luca Barsi, PhD, Rome, Italy, 00185; e-mail: barsiluca1@gmail.com
Maliarova Liudmila Volodimirivna, Assistant, Department of hygiene and social medicine, School of Medicine, V. N. Karazin Kharkiv National University, 6, Svobody sq., Kharkiv, Ukraine, 61022, e-mail: l.v.maliarova@karazin.ua, https://orcid.org/0000-0002-7902-7016
For citation:
Martynenko O, Raimondi G, Barsi L, Maliarova L. ENTROPY OF FREQUENCY DOMAIN OF HEART RATE VARIABILITY. The Journal of V. N. Karazin Kharkiv National University. Series «Medicine». 2022;45:4-11. DOI: 10.26565/2313-6693-2022-45-01
INTRODUCTION
The heart rate variability (HRV) is based on measuring (time) intervals between R-peaks (of RR-intervals) of an electrocardiogram (ECG) and plotting a rhythmogram on their basis with its subsequent analysis by various mathematical methods that are classified as Time-Domain (TD), Frequency-Domain (FD) and Nonlinear [1, 2]. There are a number of popular Nonlinear methods used in HRV analysis, such as entropy-based measures, like approximate entropy (ApEn) [3] and sample entropy (SampEn) [4]. SampEn is regarded as a modified version of ApEn, intended to solve such shortcomings as bias and relative inconsistency [4]. However, the traditional SampEn method is single-scale based and, therefore, fails to account for the multiple time scales inherent in cardiovascular systems [5-7]. Multiscale entropy (MSE) method was proposed in [7] and received much attention in the biomedical and mechanical fields [8-10]. Further MSE developing was transformed to multiscale multivariate entropy analysis [8, 10-13]. These entropy-based measures are all applied to original RRs, - that is mean their implementation for Time-Domain. Other hand the Spectral Entropy (SE) is using for Frequency-Domain: it is defined to be the Shannon entropy of the power spectral density (PSD) of the data. In article [14] the SE were estimated for healthy, thyroid and depression subjects, as well as for patients with Congestive Heart Failure (CHF) and Atrial Fibrillation (AF). It was shown the significant different of SE for all categories and ordered to increase of SE are: depression, thyroid, CHF, AF and healthy subjects. An important characteristic of Frequency-
Domain studies is sympatho-vagal balance, which has been overlooked by entropy-based analysis. The reason for this was that good entropy analysis restricted the number of existing HRV data, which is shrinking in FD and also in total spectrum parts.
Prevalence of the effective methodology of entropy analysis of FD for standard 5-min HRV records is suppressed by unsatisfactory accuracy of available methods in case of short records as we shown in [15]. Therefore, it appears there is a necessity for building a robust formula for calculating entropy for each part of spectrum in Frequency-Domain with required accuracy for a limited series of RR-intervals observed in a standard 5-minute HRV record.
MATERIALS AND METHODS
We used long-term HRV records by Massachusetts Institute of Technology -Boston's Beth Israel Hospital (MIT-BIH) from [16] (http://www.physionet.org), a freeaccess, on-line archive of physiological signals. Normal Sinus Rhythm (NSR) RR Interval Database includes beat annotation files for 54 long-term ECG recordings of subjects in normal sinus rhythm (30 men, aged 28.5 to 76, and 24 women, aged 58 to 73). Congestive Heart Failure (CHF) RR Interval Database includes beat annotation files for 29 long-term ECG recordings of subjects aged 34 to 79, with congestive heart failure (NYHA classes I, II, and III). Subjects include 8 men and 2 women; gender of the remaining 21 subjects is not known. The original electrocardiography (ECG) signals for both NSR and CHF RR interval databases were digitized at 128 Hz, and the beat annotations were obtained by automated analysis with manual review and correction.
The MIT-BIH Atrial Fibrillation (AF) Database [17] was used for our entropy-based analyzing with long and short RR's subsets. This database includes 25 long-term ECG recordings of human subjects with atrial fibrillation (mostly paroxysmal). The individual recordings are each 10 hours in duration, and contain two ECG signals each sampled at 250 samples per second with 12bit resolution over a range of ± 10 millivolts. The original analog recordings were made at Boston's Beth Israel Hospital (now the Beth Israel Deaconess Medical Center) using ambulatory ECG recorders with a typical recording bandwidth of approximately 0.1 Hz to 40 Hz.
A generalized form of the Robust Entropy Estimator (EnRE) for time series was proposed in [15] and adopted for power spectral density (PSD) of RR now:
EnRE =
m/
(Ptj) /2
where MD is median of the sequence for B value of PSD; Dij- distance between Bt andBj; A, l, m, k - estimated coefficients. Search conditions for coefficients A, l, m, k is the following:
1/ accurate approximation for known distributions of a random value;
2/ independence of EnRE from N for initial time series and for series after sorting;
3/ independence of EnRE from additive changes of mean.
After numerical researches the following coefficient values had been found: l = 3, m = 1, k = 2.
The difference between means of the two independent selections (NSR and CHF, before and after AF) has been determined by a t-test for independent samples; discriminant analysis and statistical calculations have been done by using the statistical package IBM SPSS 27.
RESULTS AND DISCUSSION
First of all, let us calculate entropy for all valuable for HRV spectral interval, namely 0-0.4 Hz. That is give us possibility to compare with existing results for Spectral Entropy: qualitatively we receive the same distribution number as [14] and significant difference (p < 0.001) between entropy averages for NSR and CHF or AF patients. Quantitatively our result is not exactly the same to [14] because we used different entropy measures: SE is based on Shannon entropy and EnRE approximated the entropy of distribution or differential entropy.
Table 1
Entropy of all spectral interval of HRV
Entropy Healthy (NSR) CHF AF
EnRE 1.77 ± 0.4* 1.13 ± 0.62 1.36 ± 0.09
SE [14] 1.95 0.85 1.15
According to [1] we define low-frequencies (LF) power spectrum components in the range of 0.04-0.15 Hz and high-frequencies (HF) power spectrum components in the range of 0.15-0.4 Hz. The sympatho-vagal balance is a simple ratio LF/HF [1]. We calculate an entropy of LF power spectrum components as eLF, entropy of HF power spectrum components as eHF and entropy based sympatho-vagal balance as a ratio eLF/eHF.
Many authors emphasize the importance of sympatho-vagal balance measures, but statistical significance makes it difficult to estimate the effects in CHF patients: for example, in [18] showed that LF/HF is significantly lower for CHF patients compare with healthy subjects, but in compare with [19], where difference in LF/HF between CHF and NSR groups is insignificant due to p = 0.175. The results of calculations of LF/HF and eLF/eHF for CHF and NSR groups are shown on the Fig. 1.
LF/HF
■ chf ■ nsr
Fig. 1. Box & Whiskers plots of LF/HF
The difference between groups are significant in both cases LF/HF and eLF/eHF with p < 0.001, but in case of eLF/eHF it is something better with t = -4.8 in compare to LF/HF where is t = -4.4. The discriminant analysis shows total classification accuracy for eLF/eHF in 79.3% (x2 = 19.4, p < 0.001) and for LF/HF in 72.4% (x2 = 16.6, p < 0.001).
eLF/eHF
o
■ chf ■ nsr
id eLF/eHF for NSR and CHF groups
More interesting is applying such entropy-based Frequencies-domain analyzing for AF patients. There is an opinion that FD analysis is unsuitable for AF and this is true in case of LF/HF, because no significant difference before and during AF due to high variation of this ratio (see Fig. 2). The entropy-based ratio eLF/eHF is suitable much better for this case, - the eLF/eHF is significantly higher during AF than before AF (p < 0.001).
Fig. 2. Box & Whiskers plots of LF/HF and eLF/eHF for AF patents (before and during AF episodes)
Fig. 3. Typical pattern of entropy of HRV power spectrum before and during atrial fibrillation episode (MIT-BIH AF Database [16]).
The Fig. 3. shows typical pattern of entropy of HRV power spectrum evolution before and during atrial fibrillation episode: each epoch on the Fig. 3. consists of short RRs records (N = 500); epoch with # '0' is the beginning of AF according to MIT-BIH reference rhythm annotations. Entropy of power spectrum does not have significant difference from mean record value under Normal rhythm intervals except 4-5 epochs before and after AF episodes: entropy begin significantly growth for about 20 minutes (or 4-5 epoch by N = 500 RRs) before AF and excides new maximal baseline during AF. The new baseline level is significantly different from previous one - before AF (p < 0.001).
Therefore, proposed generalized form for Robust Entropy Estimator EnRE for HRV power spectrum shows significant differences (p < 0.001) of total spectrum entropy and entropy-based sympatho-vagal balance for NSR and CHF groups in short records (N = 500), and presents additional advantages provided by EnRE in case of patients with atrial fibrillation.
CONCLUSIONS
Proposed in the article is generalized form for Robust Entropy Estimator EnRE for
Frequencies-domain, which allows, for time series of a limited length (standard 5-min. records), to find entropy value of HRV power spectrum (total spectrum, low- and high-frequencies bands). Parameters in generalized form for EnRE have been derived from the following criteria:
1/ accurate approximation for known distributions of a random value in ranges that represent models of RRs for heart rate variability;
2/ independence of EnRE from N for initial time series and for series after sorting;
3/ independence of EnRE from additive changes of mean.
Using the proposed EnRE for MIT-BIH database of HRV records, we show for standard 5 min. HRV records the usage of EnRE of HRV power spectrum and entropy-based sympatho-vagal balance of Normal Sinus Rhythm (NSR) and Congestive Heart Failure (CHF) cases. It is demonstrated, that, entropy-based Frequencies-domain analyzing is applicable for case of Atrial Fibrillation (AF) even during AF episodes. We showed the significant difference (p < 0.001) before and during AF for entropy of total spectrum, as well as for sympatho-vagal balance in form of eLF/eHF.
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15. Martynenko A, Raimondi G, Budreiko N. Robust Entropy Estimator for Heart Rate Variability. Klin. Inform. Telemed. 2019;14(15):67-73. DOI: 10.31071/kit2019.15.06
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ЕНТРОП1Я ЧАСТОТНОГО ДОМЕНУ ВАР1АБЕЛЬНОСТ1 СЕРЦЕВОГО РИТМУ
Мартиненко О. В.А B>C>D>E>F, Раймонд1 Д.Л'Е'Г, Барс1 Л.Е'Г, Малярова Л. B.E'F
A - концепця та дизайн дослвдження; B - 36ip даних; C - анал1з та штерпретащя даних; D - написання стат; E - редагування статп; F - остаточне затвердження статп
Вступ. Варiабельнiсть серцевого ритму (ВСР) базуеться на вимiрюваннi (часових) iнтервалiв мiж R-тками (RR-iнтервалiв) електрокардюграми (ЕКГ) i побудови на ix ochobí ритмограми з подальшим И аналiзом рiзними математичними методами, яш класиф^ються як Часова область (TD), частотна область (FD) i нелттна [1, 2]. 1снуе ряд популярних нелтшних методiв, яш використовуються в
aHani3i BCP, HanpuKnag BHMipMBaHHa Ha 0CH0Bi eHTponii, mi b ochobhomy 3acTocoByMTbca gna TD. CneKTpanbHa emponia (SE) BHKopucTOByeTbca gna HacTOTHOi o6nacTi: BOHa BH3HaHaeTbca aK eHTponia ffleHHOHa cneKTpanbHOi minbHocri noTy®HocTi (PSD) gaHux. Ba®nuBOM xapaKTepucTHKOM HacTOTHux gocnig®eHb e cHMnaro-BaranbHHH 6anaHc, aKHH paHime He BpaxoByBaBca b aHani3i Ha 0CH0Bi eHTponii. npuHHHOM ^oro 6yno Te, mo aKicHHH eHTponiHHHH aHani3 06Me®eH0 KinbKicTM icHyMHux gaHux BCP, aKi 3MeHmyMTbca y FD, a TaKO® y HacTHHax 3aranbHoro cneKTpy.
MeTa. MeTOM mei CTarri e HagaHHa HagiHHOi $opMynu gna TOHHoro o6HucneHHa eHTponii' gna nacTOTHOi o6nacri CTaHgapTHHx 5 xBunuH 3anucy BCP Ta noKa3aTH nepeBaru TaKoro nigxogy gna aHani3y CHMnaTO-BaranbHoro öanaHcy y 3gopoBux cyö'eKTiB (NSR), namemiB i3 3acTiHHOM cep^BOM HegocTaTHicTM (CHF) Ta $i6punamera nepegcepgb (AF).
MaTepianu i MeTogu. Mh BHKopucTOByBanu g0Br0CTp0K0Bi 3anucu BCP 6a3H gaHux MIT-BIH gna HopManbHoro cuHycoBoro puTMy (NSR), 3acTiHHOi cep^BOi Heg0CTaTH0CTi (CHF) i $i6punami nepegcepgb (AF).
Eyna 3anp0n0H0BaHa y3aranbHeHa $opMa HagiHHoro o^HMBaHa eHTponii' (EnRE) gna HacTOTHOi oönacTi CTaHgapTHHx 5 xb. 3anuciB BCP i noKa3aHi KnMHOBi O3HaKH EnRE.
Pi3HH^ Mi® cepegHiMH 3HaHeHHaMH gBox He3ane®Hux BuöipoK (NSR i CHF, go i nicna AF) 6yna BH3HaneHa t-TecTOM gna He3ane®Hux Bu6ipoK; gHcKpHMiHaHTHHH aHani3 i CTaTHCTUHHi po3paxyHKH BHKOHaHO 3a gonoMoroM CTaTHCTUHHoro naKeTy IBM SPSS 27.
Pe3ymTaTH. Mh o6HucnMBanu eHTponiM gna BCboro cneKTpanbHoro irnepBany BCP, a caMe 0-0,4 i nopiBHMBanu 3 icHyMHHMH pe3ynbraraMH gna cneKTpanbHOi eHTponii': aKicHO mh OTpuMyeMO TaKe ® Hucno po3noginy, aK y [14], i 3Hanymy pi3HHUM (p < 0,001) Mi® cepegHiMH 3HaneHHaMH eHTponii gna NSR Ta namemiB i3 CHF a6o AF.
Bu3HanaeMO HH3bKOHacTOTHi (LF) CKnagoBi cneKTpa n0Ty®H0CTi b giana3OHi 0,04-0,15 ^ i BHCOKOHacTOTHi (HF) KOMnoHeHTH cneKTpa n0Ty®H0CTi b giana3OHi 0,15-0,4 ^ [1]. CuMnaTO-BaranbHHH 6anaHC - ^ npocTe cniBBigHomeHHa LF/HF [1]. Mh 06HucnMeM0 empomw KOMnoHeHTiB cneKTpy n0Ty®H0CTi LF aK eLF, eHTponiM KOMnoHemiB cneKTpy n0Ty®H0CTi HF aK eHF i cuMnaTO-BaranbHHH 6anaHC Ha 0CH0Bi eHTponii aK CniBBigHomeHHa eLF/eHF.
Piзннцa Mi® rpynaMH NSR i CHF e 3HaHHOM b o6ox BunagKax LF/HF i eLF/eHF 3 p < 0,001, ane y BunagKy eLF/eHF цe gemo Kpame 3 t = -4,8 nopiBHaHO 3 LF/HF, ge t = -4,4. ^HCKpuMiHaHTHun aHani3 noKa3ye 3aranbHy TOHHicTb Knacu^iKami gna eLF/eHF y 79,3 % (x2 = 19,4, p < 0,001) i gna LF/HF y 72,4 % (X2 = 16,6, p < 0,001).
Mh 3acTOcyBanu HacTOTHHH aHani3 Ha 0CH0Bi eHTponii gna naqiemiB 3 AF i noKa3anu, mo CniBBigHomeHHa eLF/eHF 3HaHHO Bume nig Hac AF, Hi® go AF (p < 0,001). ^ np0Tune®H0 3BHHaHHOMy H^/B^, ge HeMae CTaTHCTHHHoi 3HaHymocri piзннцi Hepe3 BenuKy вapiaцiм ^oro CniBBigHomeHHa.
Bhchobkh. y CTarri 3anponoHOBaHO y3aranbHeHy $opMy HagiHHoro оцiнмвaнa eHTponii EnRE 3agna HacTOTHoro goMeHy BCP, mo go3Bonae gna HacoBux pagiB o6Me®eHoi goB®HHH (cTaHgapTHi 5-xBunuHHi 3anucu) 3HaxoguTH 3HaHeHHa eHTponii cneKTpa n0Ty®H0cri BCP (3aranbHHH cneKTp, HH3bKa i BucoKa CMyru HacTOT).
BuKopucTOByMHH 3anp0n0H0BaHy ^opMyny EnRE gna MIT-BIH 6a3H gaHux 3anuciB BCP, mh noKa3anu gna CTaHgapTHHx 5 xb. 3anuciB BCP BHKopucTaHHa EnRE cneKTpa n0Ty®H0cri BCP Ta cuMnaTO-BaranbHoro 6anaHcy Ha 0CH0Bi eHTponii y BunagKax HopManbHoro cuHycoBoro puTMy (NSR) i 3acriHHoi сepцeвоi Heg0CTaTH0CTi (CHF). np0geM0HCTp0BaH0, mo eHTponiHHHH aHani3 y HacTOTHin o6nacTi 3acTOCOBaHHH gna BunagKiB $i6pHnami nepegcepgb (AF) HaBiTb nig Hac eni3ogiB AF. Mh noKa3anu gocTOBipHy pi3HHUM (p < 0,001) go Ta nig Hac AF gna eHTponii 3aranbHoro cneKTpy, a TaKO® gna cuMnaTO-BaranbHoro 6anaHcy y $opMi eLF/eHF.
KHWHOBI CHOBA: eapia6enbnicmb серцеeого pumMy, enmponrn, nacmomnuu öoMen, 3acmiunoi cep^eoi neöocmamnocmi, $i6puM^ii nepedcepdb
HH^OPMAUja nPO ABTOPIB
MapTHHeHKo OneKcaHgp BiTaninoBHH, g.^i3-MaT.H., npo^ecop, npo^ecop Ka^egpn ririeHH Ta соцianbноl MeguunHH XapKiBCbKoro нaцiонanbноrо yHiBepcHTeTy iMeHi B. H. Kapa3iHa, MangaH CBo6ogn, 6, XapKiB, YKpaiHa, 61022, e-mail: Alexander.v.martynenko@karazin.ua, ORCID ID: https://orcid.org/0000-0002-0609-2220.
PaHMOHgu, g.Meg.H., npo^., PuMcbKHH yHiBepcHTeT ^a Canie^a (iTania), nbauHane Anbgo Mopo, 5, Phm, iTania, 00185, e-mail: gianfrancoraimondi@uniroma1.it
.H. Bapci, goKTop ^inoco^ii, Phm, iTania, 00185; e-mail: barsiluca1@gmail.com
ManapoBa .MgMHna BonogHMHpiBHa, acucTeHT Ka^egpn ririeHH Ta cоцianbноl MeguunHH XapKiBcbKoro Ha^OHanbHoro yHiBepcHTeTy iMeHi B. H. Kapa3iHa, MangaH CBo6ogu, 6, XapKiB, YKpaiHa, 61022, e-mail: l.v.maliarova@karazin.ua, https://orcid.org/0000-0002-7902-7016
Для цитування:
Мартиненко ОВ, Раймондi ДА, Бара ЛЕ, Малярова ЛВ. ЕНТРОП1Я ЧАСТОТНОГО ДОМЕНУ ВАР1АБЕЛЬНОСТ1 СЕРЦЕВОГО РИТМУ. Вюник Харкiвського нацiонального унiверситету iменi В. Н. Каразша. Серiя «Медицина». 2022;45:4-11. DOI: 10.26565/2313-6693-2022-45-01
Conflicts of interest: author has no conflict of interest to declare. Конфлжт mmepecie: вгдсутнт.
Отримано: 10.10.2022року Прийнято до друку: 20.11.2022 року Received: 10.10.2022 Accepted: 11.20.2022
